A000648 Number of alkyls C_{n+15} H_{2n+10} (Anthr.) with n carbon atoms. (Formerly M3045 N1235)

1, 3, 18, 61, 225, 716, 2272, 6826, 20238, 58552, 167625, 473929, 1330490, 3709591, 10296336, 28466065, 78481065, 215878221, 592832960, 1625887129, 4454936029, 12198071235, 33383810793, 91336813784, 249851178964, 683421422654

Offset

0,2

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..25.

G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; line 15 of Table I.

G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I, line 15. (Annotated scanned copy)

Formula

G.f.: A(x) = (r(x)^10 + r(x)^2*r(x^2)^4 + 2*r(x^2)^5)/4, r(x) = A000598(x).

Mathematica

terms = 26; (* r = g.f. for A000598 *) r[_] = 0; Do[r[x_] = 1 + (1/6)*x*(r[x]^3 + 3*r[x]*r[x^2] + 2*r[x^3]) + O[x]^terms // Normal, terms];
A[x_] = (r[x]^10 + r[x]^2*r[x^2]^4 + 2*r[x^2]^5)/4 + O[x]^terms;
CoefficientList[A[x], x] (* Jean-François Alcover, Jan 10 2018 *)

Crossrefs

Cf. A000649.

Sequence in context: A074439 A299031 A210366 * A235988 A253942 A317404

Adjacent sequences: A000645 A000646 A000647 * A000649 A000650 A000651

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved